Cuerno literally translates to "horn," like one on an animal. However, it has a famous double meaning in Spanish slang.
The idiom "poner los cuernos" (literally "to put the horns on") means to cheat on a romantic partner. In "TU NAME", the singer reveals the reason for the breakup in one line: "Todo por un cuerno" (All because of an infidelity), making this a powerful and essential piece of slang to learn.
This is the ultimate getting-over-your-ex song. Fuerza Regida doesn't waste any time with sad feelings. The singer kicks things off by telling his ex, "Ya no te topo, ya vete a la fregada" (I don't see you anymore, go to hell). He's moved on in a big way, claiming he found someone "como tú pero mejor" (like you but better) and is now buying her all the things he never bought for his ex.
He says the breakup happened "Todo por un cuerno" (All because of a horn), suggesting she cheated. Now, his life is a constant party with new women like "la Briana, Juliana y la Tania". The chorus is the final blow, where he repeats that he's at a party and has completely forgotten his ex's identity: "No te conozco, mami, mami / Se me olvidó tu name" (I don't know you, mami, mami / I forgot your name). He's not just over her; he's erased her.